A C E
Answers | Investigation 1 Review Day: 1/5 pg. 22 #10, 11, 36, 37, 38 10. a. Mix Y is the most appley given it has the highest concentrate-­‐to-­‐juice ratio. The ratios of concentrate to juice are the following: Mix W = 5 : 13, Mix X = 3 : 9, Mix Y = 6 : 15, and Mix Z = 3 : 8. b. Mix W = 135 , Mix X = 39 = 31 , Mix Y = 156 = 52 ÷ Mix Z = 38 c. Mix W ≈ 38.5%, Mix X ≈ 33.3%, Mix Y = 40%, Mix Z = 37.5% d. Mix W: 138 cup water and 135 cup concentrate 11. Examine these statements about the apple juice mixes in Exercise 1. Decide whether each is accurate. Give reasons for your answers. a. Not accurate since both water and concentrate contribute to the least appley taste. A mix with 9 cups of water that had 1 cup of concentrate would taste much less appley. b. Not accurate. Mix Y is the most appley. Also, being the most appley is not dependent on the difference between the two ingredients, but on the fraction or percent of concentrate of the total cups of liquid. c. Accurate. Mix Y is the most appley because it has the greatest ratio of concentrate to water. d. Not accurate. The taste is determined by the ratio of concentrate to water. Since Mix Y has more concentrate per cup of water, it will have the most appley taste. 36. B (0.6 times the scale factor of 1.5 equals 0.9.) 37. No. It means that for every 7 people that responded to the survey, 4 of them watched the Super Bowl. If the survey only sampled 7 people, then 4 of them watched. But if the survey sampled 7,000 people, about 4,000 watched. Four sevenths means that 74 of the number sampled, whatever that number is, 38. watched. For example, if the survey sampled 100 people, 74 × 100 would be 57.14. a. One piece will be 1.5 inches, and the other will be 3.5 inches. A ratio of 3 : 7 also means that one piece will be 0.3 of the fruit bar and the other piece will be 0.7 of the fruit bar. Thus, 0.3 × 5 = 1.5 and 0.7 × 5 = 3.5. b. One piece will be 3 inches long, and the other will be 2 inches long (60% = 0.6, 0.6 × 5 = 3). c. One piece will be 3 inches long, and the other will be 2 inches long. 1/6 pg. 23 #13 -­‐ 17 13. a. 4 : 1, part-­‐to-­‐part b. 1 : 5, part-­‐to-­‐whole c. 4 : 5, part-­‐to-­‐whole 14. a. Ratio of concentrate to juice: 12
= 51 60
b. Ratio of concentrate to water: 123 = 41 c. Ratio of water to juice: d. This fraction does not represent a ratio from this situation. 2
21
2
= 54 15. a. Less concentrated (less grapefruity); Using the original mix, and scaling by 3, 3 cans of concentrate should be mixed with 12 cans of water. So, 15 cans of water makes the mix more watered down. b. The same concentration as the original; As stated in part (a), 12 cans of water plus 3 cans of concentrate would give 15 cans of juice. c. More concentrated (more grapefruity); Using the original mix and scaling by 2.5, 10 cans of water should be mixed with 2.5 cans of concentrate. Students might say the same concentration if they are mistakenly thinking of scaling as additive, that is, adding 6 cans of water and 6 cans of concentrate will give the same concentration. If students say this, you can point out that the ratio of concentrate to water in Mix C is over 21 , but the original is less than 21 . d. Less concentrated (less grapefruity); Using a scale factor of 41 , 41 can of concentrate should be mixed with 1 can of water. 16. The mixture will be the same as the original. Because the original two mixtures were the same ratio as the original mixing instructions, adding these two batches together will result in the same ratio. Interestingly, fractional notation may cause (10 + 8)
some difficulty if students consider this problem as 41 + 41 instead of (32
= 41 . + 40)
17. a. b. c. d. Scale Factor is 24; 4 × 24 = 96 cans of water. Scale Factor is 5; 24 × 5 = 120 cans of juice. Scale Factor is 245 = 4.8; 4.8 × 4 = 19.2 cans of water. Scale Factor is 245 = 4.8; 4.8 × 1 = 4.8 or 4 54 cans of water. 1/7 pg. 29 #42, 44 -­‐ 46 42. 44. 45. a. b. c. d. e. f. 9 11, or any number greater than 10 13, or any number greater than 12 4.5, or any number greater than 4.5 9, or any number greater than 9 28 Possible answer: 34 > 32 , 34 is greater because it is closer to 1. Its decimal equivalent is 0.75 as compared to about 0.67, the decimal approximation of 32 . 46. Possible answer: 21 > 0.25 (0.5 > 0.25). 47. 4
5
11
< 12
(0.8 < 0.916…) 1/8 pg. 25 #19, 20, 57, 58, 59, 60 19. a. 6 miles; Using equivalent ratios, 151 = 90x The scale factor is 6. b. About 4.3 miles; The scale factor is 133 , or 4.333… 20. a. 6.5 miles; Using equivalent ratios, 0.25
= 26x . The scale factor is 26. 1
57. 58. 59. b. H A a. b. c. d. 20 miles; Using equivalent ratios, 0.25
= 5x . The scale factor is 20. 1
60. a. b. c. d. = = 6
= 128 = 14
9
21
4 = 5 = 6 75
90
60
6 = 15 = 24 4
10
16
9; The scale factor is 3 (12 ÷ 4 = 3 and 3 × 3 = 9). 10; The numerator must be greater than 9 because 129 = 34 . 8; 129 = 34 , so the numerator must be less than 9. 16; The scale factor is 34 ⎛⎜ 12 ÷ 9 = 34 and 34 × 12 = 16 ) . 6
8
9
12
12
16
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